Cette étude porte sur la modélisation de la durée de vie à l'écaillage des barrières thermiques pour aubes de turbines aéronautiques. La caractérisation expérimentale de l'adhérence du revêtement combine l'identification de la durée de vie - qualifiée par l'écaillage macroscopique de la céramique - à une caractérisation de l'endommagement à l'échelle de la microstructure du revêtement et en particulier à la dégradation des interfaces céramique / oxyde / métal. Des essais de compression uniaxiale sur des éprouvettes en AM1 revêtues NiAlPt et YSZ par EB-PVD, vieillies en fatigue thermique et mécano-thermique permettent d'estimer l'adhérence du revêtement. Ces essais sont complétés par des essais de propagation du délaminage interfacial par compression. Un essai original de compression in situ en laminographie aux rayons X a également permis d'analyser l'écaillage et la propagation du front de délaminage. Tous ces essais sont instrumentés et équipés de moyens d'observation permettant de réaliser des mesures de surfaces délaminées ou écaillées et de déterminer leur évolution en fonction des déformations locales mesurées.Une analyse microstructurale complète l'étude afin de comprendre l'influence du vieillissement thermique ou mécano-thermique sur l'évolution de l'endommagement du système. Cette analyse porte sur les mécanismes d'oxydation, de diffusion, de changement de phase principalement dans l'oxyde et la sous-couche. Elle est complétée par l'étude de l'ondulation de surface au cours du cyclage thermique, phénomène de « rumpling », et de ses conséquences, notamment au niveau de l'endommagement global de l'interface et de son adhérence. Le lien entre endommagement de l'interface à l'échelle d'imperfections de rugosité (quelques microns) et de la propagation d'une fissure d'interface (quelques dizaines à quelques centaines de microns) est analysé numériquement par la méthode des zones cohésives.Ces deux études complémentaires ont permis d'établir un modèle phénoménologique de durée de vie à l'écaillage. Celui-ci se base sur une estimation de l'énergie contenue dans la couche de céramique comparée à la valeur théorique d'énergie critique à rupture obtenue par un modèle d'endommagement, fonction de l'oxydation et des paramètres de chargement mécano-thermique. Ce modèle est implémenté en post-processeur d'un calcul par éléments finis facilitant son utilisation industrielle. / This study aims to model lifetime of thermal barrier coating (TBC) used on aircraft turbine blades. Experimental characterization of the coating adherence combines the lifetime identification – described by macroscopic spallation of the ceramic – with damage estimation trough the analysis of the influence of the microstructure of the coating and evolutions of interfaces ceramic / oxide / metal.Adherence of the ceramic is assessed using uniaxial mechanical compressive tests on AM1 specimen coated with NiAlPt bond coat and EB-PVD yttria stabilized zirconia varying the thermal and thermo-mechanical fatigue ageing conditions. Those tests are completed with analysis of interfacial crack propagation. A pioneering in situ compressive test using X-ray laminography has also been developed to analyze spallation and further delamination. The use of in-situ surface imaging by CCD cameras has enabled measurement of delaminated or spalled areas as function of measured local strain.The influence of thermal or thermo mechanical ageing on damage evolution of TBCs is studied through a microstructural analysis. Oxidation, diffusion and phase transformation mechanisms in the alumina and the bond coat are main parts of this analysis. Moreover the oxide rumpling and its consequences have been detailed, particularly through the measurement of global interfacial damage and adherence evolution. The link between interfacial damage at the scale of local defects (few microns) and the propagation of an interfacial crack (from tens to hundreds of microns) is numerically analyzed with a cohesive zone model.Those two spatial length of analysis were used to build a phenomenological lifetime model to spallation. This model was based on the assessment of the elastic strain energy stored in the ceramic layer and it comparison to fracture energy. A damage model is used to model the fracture strain energy evolution as a function of oxidation and thermo mechanical loading. This model is implemented in post processor of a FEM analysis, making its industrial use easier.

Les fibres naturelles telles que le lin, le chanvre, le bambou ou la miscanthus sont de plus en plus utilisées pour renforcer les composites industriels afin de réduire le poids, le coût et l’impact environnemental des produits. Elles remplacent les composites conventionnels tels que les composites à base de résine polymère et fibres synthétiques. Les méthodes de parachèvement par usinage de ces produits agrocomposites demeurent un verrou technologique et un défi scientifique. Ceci est dû principalement à la structure complexe des fibres végétales constituée de cellulose et issue des feuilles ou des tiges de plantes cultivées. Ce travail de thèse propose une analyse multiéchelle du comportement à la coupe de ces matériaux renouvelables qui exploite un procédé 2D de coupe orthogonale et un procédé 3D de coupe par fraisage. L’objectif étant de mieux appréhender les mécanismes physiques majeurs activés par le processus d’enlèvement de matière des agrocomposites. Aussi, pour identifier les effets d’échelle observés en usinage, une caractérisation tribo-mécanique des agrocomposites stratifiés par nanoindentation et rayage ainsi que des essais mécaniques spécifiques ont été réalisés. Les fibres végétales se différencient des fibres synthétiques par une flexibilité transversale qui leur confère une grande capacité à se déformer lors du contact avec l’outil de coupe. Ainsi, la rigidité mécanique du contact outil/matière contrôle ici la coupe par cisaillement plastique des fibres végétales et, par conséquence, la qualité de la surface usinée des agrocomposites. Les fibres végétales, associées à une matrice polymère thermoplastique, présentent par ailleurs un comportement mécanique élastoplastique avec un endommagement ductile lorsqu’elles sont sollicitées suivant leur direction transversale. Ceci explique la production de copeaux continus en usinage par opposition aux composites synthétiques conventionnels. Les comportements mécanique et tribologique des fibres végétales en usinage sont fonction de l’échelle de contact. Ceci explique le caractère multiéchelle de la coupe des agrocomposites dont l’usinabilité est intiment liée à la taille du renfort fibreux. / Natural fibers such as flax, hemp, bamboo or miscanthus are increasingly used as fibrous reinforcement in order to reduce the weight, the cost and the environmental impact of products. They replace the conventional composites based on polymer resin and synthetic fibers. The finishing operations by machining of these biocomposite products remain a technological issue and a scientific challenge. This is mainly due to the complex structure of natural fibers composed of cellulose and extracted from plant leaf or plant stem. This research work provides a multiscale analysis of cutting behavior of these renewable materials in 2D orthogonal cutting and 3D milling processes. The primary objective is to better understand the major physical mechanisms activated by the material removal process of biocomposites. Furthermore, to identify the scale effects observed in machining, a tribo-mechanical characterization of stratified biocomposites by nanoindentation and scratch as well as specific mechanical tests were carried out. Natural fibers are distinguished from synthetic fibers by a transverse flexibility, which enable them good ability to deform upon contact with the cutting tool. Thus, the mechanical tool/material contact stiffness controls the cutting by plastic shearing of plant fibers and, consequently, it controls the quality of the biocomposite-machined surfaces. Otherwise, natural fibers, associated with a thermoplastic polymer matrix, have an elastoplastic behavior with a ductile damage when they are stressed in their transverse direction. This explains the production of continuous chips when machining biocomposites, unlike conventional synthetic composites. The mechanical and tribological behaviors of plant fibers in machining are dependent on the contact scale. This explains the multiscale cutting character of biocomposites where the machinability is intimately related to the size of the fibrous reinforcement.

Real-time sensing brings the proliferation of big data that contains rich information of complex systems. It is well known that real-world systems show high levels of nonlinear and nonstationary behaviors in the presence of extraneous noise. This brings significant challenges for human experts to visually inspect the integrity and performance of complex systems from the collected data. My research goal is to develop innovative methodologies for modeling and optimizing complex systems, and create enabling technologies for real-world applications. Specifically, my research focuses on Mining Dynamic Recurrences in Nonlinear and Nonstationary Systems for Feature Extraction, Process Monitoring and Fault Diagnosis. This research will enable and assist in (i) sensor-driven modeling, monitoring and optimization of complex systems; (ii) integrating product design with system design of nonlinear dynamic processes; and (iii) creating better prediction/diagnostic tools for real-world complex processes. My research accomplishments include the following. (1) Feature Extraction and Analysis: I proposed a novel multiscale recurrence analysis to not only delineate recurrence dynamics in complex systems, but also resolve the computational issues for the large-scale datasets. It was utilized to identify heart failure subjects from the 24-hour heart rate variability (HRV) time series and control the quality of mobile-phone-based electrocardiogram (ECG) signals. (2) Modeling and Prediction: I proposed the design of stochastic sensor network to allow a subset of sensors at varying locations within the network to transmit dynamic information intermittently, and a new approach of sparse particle filtering to model spatiotemporal dynamics of big data in the stochastic sensor network. It may be noted that the proposed algorithm is very general and can be potentially applicable for stochastic sensor networks in a variety of disciplines, e.g., environmental sensor network and battlefield surveillance network. (3) Monitoring and Control: Process monitoring of dynamic transitions in complex systems is more concerned with aperiodic recurrences and heterogeneous types of recurrence variations. However, traditional recurrence analysis treats all recurrence states homogeneously, thereby failing to delineate heterogeneous recurrence patterns. I developed a new approach of heterogeneous recurrence analysis for complex systems informatics, process monitoring and anomaly detection. (4) Simulation and Optimization: Another research focuses on fractal-based simulation to study spatiotemporal dynamics on fractal surfaces of high-dimensional complex systems, and further optimize spatiotemporal patterns. This proposed algorithm is applied to study the reaction-diffusion modeling on fractal surfaces and real-world 3D heart surfaces.

This thesis study two promising methods used to define the multiscale CAPM - the wavelet-based decomposition and the fractal regression. Their estimates, obtained on monthly excess return on ten portfolios formed on beta in the US market, are compared in the period from November 2000 to October 2020 and, subsequently, in the period from November 1965 to October 2020. In the first period, the multiscale beta is not significantly different from the original single-scale beta for most of the portfolios. Contrary, both methods uncover significant multiscale behavior of the beta in the second period. Specifically, the high-beta portfolios have higher multiscale beta at longer investment horizons, mainly at wavelet scale 3 and scales 12-24 of the fractal regression. Overall, both methods deliver consistent results, and seem suitable for extending the CAPM with an investment horizon. JEL Classification Keywords G12, C20 CAPM, asset pricing, multiscale analysis, wavelets, fractal regression Title Investment horizon in the CAPM: A comparison of a wavelet-based decomposition and the fractal regression

Many machine learning problems involve dealing with a large amount of high-dimensional data across diverse domains. In addition, annotating or labeling the data is expensive as it involves significant human effort. This dissertation explores a joint solution to both these problems by exploiting the property that high-dimensional data in real-world application domains often lies on a lower-dimensional structure, whose geometry can be modeled as a graph or manifold. In particular, we propose a set of novel manifold-alignment based approaches for transfer learning. The proposed approaches transfer knowledge across different domains by finding low-dimensional embeddings of the datasets to a common latent space, which simultaneously match corresponding instances while preserving local or global geometry of each input dataset. We develop a novel two-step transfer learning method called Procrustes alignment. Procrustes alignment first maps the datasets to low-dimensional latent spaces reflecting their intrinsic geometries and then removes the translational, rotational and scaling components from one set so that the optimal alignment between the two sets can be achieved. This approach can preserve either global geometry or local geometry depending on the dimensionality reduction approach used in the first step. We propose a general one-step manifold alignment framework called manifold projections that can find alignments, both across instances as well as across features, while preserving local domain geometry. We develop and mathematically analyze several extensions of this framework to more challenging situations, including (1) when no correspondences across domains are given; (2) when the global geometry of each input domain needs to be respected; (3) when label information rather than correspondence information is available. A final contribution of this thesis is the study of multiscale methods for manifold alignment. Multiscale alignment automatically generates alignment results at different levels by discovering the shared intrinsic multilevel structures of the given datasets, providing a common representation across all input datasets.

The emerging field of nanomechanics is providing a new focus in the study of the mechanics of materials, particularly in simulating fundamental atomic mechanisms involved in the initiation and evolution of damage. Simulating fundamental material processes using first principles in physics strongly motivates the formulation of computational multiscale methods to link macroscopic failure to the underlying atomic processes from which all material behavior originates. A combined concurrent and sequential multiscale methodology is developed to analyze fracture mechanisms across length scales. Unique characterizations of grain boundary fracture mechanisms in an aluminum material system are performed at the atomic level using molecular dynamics simulation and are mapped into cohesive zone models for continuum modeling within a finite element framework. Fracture along grain boundaries typically exhibit a dependence of crack tip processes (i.e. void nucleation in brittle cleavage or dislocation emission in ductile blunting) on the direction of propagation due to slip plane orientation in adjacent grains. A new method of concurrently coupling molecular dynamics and finite element analysis frameworks is formulated to minimize the overall computational requirements in simulating atomistically large material regions. A sequential multiscale approach is advanced to model microscale polycrystal domains in which atomistically-based cohesive zone parameters are incorporated into special directional decohesion finite elements that automatically apply appropriate ductile or brittle cohesive properties depending on the direction of crack propagation. The developed multiscale analysis methodology is illustrated through a parametric study of grain boundary fracture in three-dimensional aluminum microstructures. / Ph. D.

Plane strain transient finite thermomechanical deformations of heat-conducting particulate composites comprised of circular tungsten particulates in nickel-iron matrix are analyzed using the finite element method to delineate the initiation and propagation of brittle/ductile failures by the nodal release technique. Each constituent and composites are modeled as strain hardening, strain-rate-hardening and thermally softening microporous materials. Values of material parameters of composites are derived by analyzing deformations of a representative volume element whose minimum dimensions are determined through numerical experiments. These values are found to be independent of sizes and random distributions of particulates, and are close to those obtained from either the rule of mixtures or micromechanics models. Brittle and ductile failures of composites are first studied by homogenizing their material properties; subsequently their ductile failure is analyzed by considering the microstructure. It is found that the continuously varying volume fraction of tungsten particulates strongly influences when and where adiabatic shear bands (ASB) initiate and their paths. Furthermore, an ASB initiates sooner in the composite than in either one of its constituents. We have studied the initiation and propagation of a brittle crack in a precracked plate deformed in plane strain tension, and a ductile crack in an infinitely long thin plate with a rather strong defect at its center and deformed in shear. The crack may propagate from the tungsten-rich region to nickel-iron-rich region or vice-a-versa. It is found that at the nominal strain-rate of 2000/s the brittle crack speed approaches Rayleigh's wave speed in the tungsten-plate, the nickel-iron-plate shatters after a small extension of the crack, and the composite plate does not shatter; the minimum nominal strain-rate for the nickel-iron-plate to shatter is 1130/s. The ductile crack speed from tungsten-rich to tungsten-poor regions is nearly one-tenth of that in the two homogeneous plates. The maximum speed of a ductile crack in tungsten and nickel-iron is found to be about 1.5 km/s. Meso and multiscale analyses have revealed that microstructural details strongly influence when and where ASBs initiate and their paths. ASB initiation criteria for particulate composites and their homogenized counterparts are different. / Ph. D.

The Bonneville Basin encompasses an area that was covered by ancient Lake Bonneville and which today lies within the Great Basin province. The Bonneville Basin is distinguished geologically by its characteristic parallel north-south mountain ranges that are separated by broad, alluviated desert basins and valleys. Benches and other shoreline features of ancient Lake Bonneville prominently mark the steep, gravelly slopes of these ranges. Numerous artesian desert springs are present at the base of the mountains and in the valley floors that form various sizes of both isolated wetlands and wetland complexes. Many these wetlands are some of the most unique and currently some of the most threatened wetlands in the United States. Several aquatic species and communities have maintained an existence as relict populations and communities in these wetlands since the receding of Lake Bonneville over 10,000 years ago. For example, Hershler has described 58 previously undescribed species of hydrobiid snails, 22 of which are endemic to single locations. Like hydrobiid snails, numerous other species, such as the least chub, Iotichthys phlegethontis and the Columbia spotted frog, Rana luteioventris, depend on these wetlands for their continued existence, many of which are already imperiled. The continued decline and loss of these wetlands would further push many of these species toward endangerment and/or extinction. Several factors have already eliminated or altered many of these habitats including capping and filling,water depletions, agricultural practices, livestock grazing, and introduction of nonnative species. In recent years, the significant loss and degradation of wetlands resulting in sensitive species designations have provided impetus for resource agencies to develop and implement management plans to conserve and protect these vital ecosystems. One problem facing appropriate management is the lack of biological information for determining which wetlands should receive protection priorities based on the presence of viable, functioning characteristics. The purpose of this dissertation project was to obtain biological information needed to support defensible decisions concerning conservation, protection, acquisition, restoration, and mitigation of the artesian springs in the Bonneville Basin. The primary objectives of this project were to 1) Develop bioassessment procedures for artesian wetlands of the Bonneville Basin using macroinvertebrates and 2) Determine patterns of community composition and diversity for macroinvertebrates and metaphyton algae at multiple scales in Bonneville Basin artesian wetlands.

Ein metrischer Graph mit einem selbstadjungierten, negativen Laplace-Operator wird Quantengraph genannt. In dieser Arbeit werden Transporteigenschaften zufälliger Laplace-Operatoren betrachtet. Dazu wird die Multiskalenanalyse (MSA) von euklidischen Räumen auf metrische Graphen angepasst. Eine Überdeckung der metrischen Graphen wird aus gleichmäßig polynomiellem Wachstum und der gleichmäßigen Beschränkung der Kantenlängen gewonnen. Als Hilfsmittel für die MSA werden eine Combes-Thomas-Abschätzung und eine Geometrische Resolventenungleichung bewiesen. Zusammen mit einer Wegner-Abschätzung und der Existenz von verallgemeinerten Eigenfunktionen wird mittels der modifizierten MSA spektrale Lokalisierung (d.h. reines Punktspektrum) mit polynomiell fallenden Eigenfunktionen am unteren Rand des Spektrums für negative Laplace-Operatoren mit zufälligem Potential geschlossen. Dabei sind alle Randbedingungen, die eine nach unten beschränkten Operator liefern, wählbar. / We prove spectral localization for infinite metric graphs with a self-adjoint Laplace operator and a random potential. Therefor we adapt the multiscale analysis (MSA) from the euclidean case to metric graphs. In the MSA a covering of the graph is needed which is obtained from a uniform polynomial growth of the graph. The geometric restrictions of the graph contain a uniform bound on the edge lengths. As boundary conditions we allow all settings which give a lower bounded self-adjoint operator with an associated quadratic form. The result is spectral localization (i.e. pure point spectrum) with polynomially decaying eigenfunctions in a small interval at the ground state energy.

This dissertation introduces new methodologies for the analysis of neural spike trains. Biological properties of the nervous system, and how they are reflected in neural data, can motivate specific analytic tools. Some of these biological aspects motivate multiscale frameworks, which allow for simultaneous modelling of the local and global behaviour of neurons. Chapter 1 provides the preliminary background on the biology of the nervous system and details the concept of information and randomness in the analysis of the neural spike trains. It also provides the reader with a thorough literature review on the current statistical models in the analysis of neural spike trains. The material presented in the next six chapters (2-7) have been the focus of three papers, which have either already been published or are being prepared for publication. It is demonstrated in Chapters 2 and 3 that the multiscale complexity penalized likelihood method, introduced in Kolaczyk and Nowak (2004), is a powerful model in the simultaneous modelling of spike trains with biological properties from different time scales. To detect the periodic spiking activities of neurons, two periodic models from the literature, Bickel et al. (2007, 2008); Shao and Li (2011), were combined and modified in a multiscale penalized likelihood model. The contributions of these chapters are (1) employinh a powerful visualization tool, inter-spike interval (ISI) plot, (2) combining the multiscale method of Kolaczyk and Nowak (2004) with the periodic models ofBickel et al. (2007, 2008) and Shao and Li (2011), to introduce the so-called additive and multiplicative models for the intensity function of neural spike trains and introducing a cross-validation scheme to estimate their tuning parameters, (3) providing the numerical bootstrap confidence bands for the multiscale estimate of the intensity function, and (4) studying the effect of time-scale on the statistical properties of spike counts. Motivated by neural integration phenomena, as well as the adjustments for the neural refractory period, Chapters 4 and 5 study the Skellam process and introduce the Skellam Process with Resetting (SPR). Introducing SPR and its application in the analysis of neural spike trains is one of the major contributions of this dissertation. This stochastic process is biologically plausible, and unlike the Poisson process, it does not suffer from limited dependency structure. It also has multivariate generalizations for the simultaneous analysis of multiple spike trains. A computationally efficient recursive algorithm for the estimation of the parameters of SPR is introduced in Chapter 5. Except for the literature review at the beginning of Chapter 4, the rest of the material within these two chapters is original. The specific contributions of Chapters 4 and 5 are (1) introducing the Skellam Process with Resetting as a statistical tool to analyze neural spike trains and studying its properties, including all theorems and lemmas provided in Chapter 4, (2) the two fairly standard definitions of the Skellam process (homogeneous and inhomogeneous) and the proof of their equivalency, (3) deriving the likelihood function based on the observable data (spike trains) and developing a computationally efficient recursive algorithm for parameter estimation, and (4) studying the effect of time scales on the SPR model. The challenging problem of multivariate analysis of the neural spike trains is addressed in Chapter 6. As far as we know, the multivariate models which are available in the literature suffer from limited dependency structures. In particular, modelling negative correlation among spike trains is a challenging problem. To address this issue, the multivariate Skellam distribution, as well as the multivariate Skellam process, which both have flexible dependency structures, are developed. Chapter 5 also introduces a multivariate version of Skellam Process with Resetting (MSPR), and a so-called profile-moment likelihood estimation of its parameters. This chapter generalizes the results of Chapter 4 and 5, and therefore, except for the brief literature review provided at the beginning of the chapter, the remainder of the material is original work. In particular, the contributions of this chapter are (1) introducing multivariate Skellam distribution, (2) introducing two definitions of the Multivariate Skellam process in both homogeneous and inhomogeneous cases and proving their equivalence, (3) introducing Multivariate Skellam Process with Resetting (MSPR) to simultaneously model spike trains from an ensemble of neurons, and (4) utilizing the so-called profile-moment likelihood method to compute estimates of the parameters of MSPR. The discussion of the developed methodologies as well as the ``next steps'' are outlined in Chapter 7.